Geodesic
On separable group rings
Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 104-111.

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Let G be a finite non-abelian group R a ring with 1, and G― the inner automorphism group of the group ring RG over R induced by the elements of G. Then three main results are shown for the separable group ring RG over R: (i) RG is not a Galois extension of (RG)G― with Galois group G― when the order of G is invertible in R, (ii) an equivalent condition for the Galois map from the subgroups H of G to (RG)H by the conjugate action of elements in H on RG is given to be one-to-one and for a separable subalgebra of RG having a preimage, respectively, and (iii) the Galois map is not an onto map.
Keywords: separable extensions, group rings
Mots-clés : Galois extensions, Galois algebras, group algebras. 
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     author = {George Szeto and Lianyong Xue},
     title = {On separable group rings},
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     year = {2010},
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George Szeto; Lianyong Xue. On separable group rings. Algebra and discrete mathematics, Tome 10 (2010) no. 1, pp. 104-111. https://geodesic-test.mathdoc.fr/item/ADM_2010_10_1_a9/